A quantitative Selberg’s lemma

  • Tsachik Gelander

    Northwestern University, Evanston, USA
  • Raz Slutsky

    Weizmann Institute of Science, Rehovot, Israel; University of Oxford, Oxford, UK
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Abstract

We show that an arithmetic lattice  in a semi-simple Lie group  contains a torsion-free subgroup of index where is the co-volume of the lattice. We prove that  is polynomial in general and poly-logarithmic under the generalized Riemann hypothesis (GRH). We then show that this poly-logarithmic bound is almost optimal, by constructing certain lattices with torsion elements of order .

Cite this article

Tsachik Gelander, Raz Slutsky, A quantitative Selberg’s lemma. Groups Geom. Dyn. (2025), published online first

DOI 10.4171/GGD/865